Transcript
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EXAMPLE 9.2 – Part I
PCI Bridge Design Manual
EXAMPLE 9.2 – Part I
PCI Bridge Design Manual
BULB “T” (BT-72)
THREE SPANS, COMPOSITE DECK
LRFD SPECIFICATIONS
Materials
copyrighted
by
Precast/Prestressed
Concrete
Institute,
2011.
All
rights
reserved.
Unauthorized
duplication
of
the material
or
presentation
prohibited.
BRIDGE LAYOUT - LongitudinalBRIDGE LAYOUT - Longitudinal
Continuous for Live Load
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BRIDGE LAYOUT – Cross SectionBRIDGE LAYOUT – Cross Section
DESIGN SPECIFICATIONSDESIGN SPECIFICATIONS
• LRFD – 5th Edition (2010)
• HL-93 Truck Loading
• No Skew
• Composite Deck
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DESIGN SPECIFICATIONSDESIGN SPECIFICATIONS
• Concrete:
– f c’ = 7.0 ksi @ 28 days
– f ci’ = 5.5 ksi @ release
– wc = 0.150 kcf
– Ecb = 33000w1.5 (f c’)
0.5 (LRFD 5.4.2.4)
= 33000(0.150)1.5(7.0)0.5 = 5072 ksi
• Prestressing Steel:
– GR 270 (f pu = 270 ksi; f py = 243 ksi) – ½” strand (Ap = 0.153 in
2 / strand)
– Ep = 28500 ksi
DESIGN SPECIFICATIONSDESIGN SPECIFICATIONS
• Mild Steel
– GR 60 (f y = 60 ksi)
– Es = 29000 ksi
• Future Wearing Surface
– 2” thick
– wws =0.150 kcf • Barriers
– New Jersey type
– 0.300 k/ft
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DESIGN SPECIFICATIONSDESIGN SPECIFICATIONS
• Deck
– 7.5” Structural thickness
– 0.5” wearing surface
– Total thickness = 8”
– f c’ = 4.0 ksi @ 28 days
– wc = 0.150 kcf
– Ecs = 33000w1.5 (f c’)
0.5 (LRFD 5.4.2.4)
= 33000(0.150)1.5(4)0.5 = 3 834 ksi
• Note – LRFD uses kip, inch, foot units in
formulae
CONTINUOUS FOR LL PRECAST BRIDGESCONTINUOUS FOR LL PRECAST BRIDGES
• Precast beams are made in a factory
and shipped to site. The beam is set on
simple supports – beam carries self
weight and prestressing force as a
simple beam.
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CONTINUOUS FOR LL PRECAST BRIDGESCONTINUOUS FOR LL PRECAST BRIDGES
The deck is formed and poured. Since the
beams are NOT shored, the beams carry the
deck load as simple beams.
CONTINUOUS FOR LL PRECAST BRIDGESCONTINUOUS FOR LL PRECAST BRIDGES
The deck is cast continuous over the piers. When the
deck hardens, a continuous structure is formed. The
negative moment connection is usually made with
non-prestressed steel over the piers. Thus, the
negative moment region is conventionally
reinforced.
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CONTINUOUS FOR LL PRECAST BRIDGESCONTINUOUS FOR LL PRECAST BRIDGES
• Once the deck hardens and continuity isestablished, any superimposed dead load
(asphalt surfaces, barriers, utilities) is carried by
the beams as a continuous structure.
• All live load is carried as a continuous structure.
CONTINUOUS FOR LL PRECAST BRIDGESCONTINUOUS FOR LL PRECAST BRIDGES
• After the slab is poured, the beams will
continue to creep and shrink; cambering
up.
• Temperature will also cause camber.
• Positive moments will form causing
cracking.
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CONTINUOUS FOR LL PRECAST BRIDGESCONTINUOUS FOR LL PRECAST BRIDGES
• A positive moment connection is
required. The requirements for this will
be discussed later. (LRFD 5.14.1.4)
CONTINUOUS FOR LL PRECAST BRIDGESCONTINUOUS FOR LL PRECAST BRIDGES
• It is thought that creep and shrinkage
will redistribute dead load, so some
states design using simple spans for all
dead load and assuming a continuous
bridge for live load only.
• Some states completely ignore the
continuity and design as simple span forall loads.
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DESIGN SPANSDESIGN SPANS
• Beams:
– Overall Length• 110 ft. end spans
• 119 ft center span
– Design Spans –Simple Span beam• 109 ft. end spans
• 118 ft. center span
– Design Spans – Continuous Beam• 110 ft. end spans
• 120 ft. center span
PROPERTIES OF BT-72PROPERTIES OF BT-72
A = 767 in.2
h = 72 in.
I = 545 894 in.4
yb = 36.60 in.
yt = 35.40 in.
Sb = 14 915 in.3
St = 15 421 in.3
w = 0.799 k/ft
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PROPERTIES OF COMPOSITE
BT-72
PROPERTIES OF COMPOSITE
BT-72
Ecs = 3834 ksi Ecb = 5072 ksi (prev. defined)
Modular ratio: n = Ecs /Ecb = 3834/5072 = 0.7559
LRFD 4.6.2.6.1 (NEW IN 2009):
The effect ive flange width is now the TRIBUTARY
AREA:
bf = 144 inches
PROPERTIES OF COMPOSITE
BT-72
PROPERTIES OF COMPOSITE
BT-72
Note: ½ inch haunchassumed.
Shaded area is
transformed.
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PROPERTIES OF COMPOSITE BT-72PROPERTIES OF COMPOSITE BT-72
Transformed Flange Width =
(Effect ive Flange Width)*n = 144(0.756)= 108.9 in.
Transformed Flange Area = 108.9” (7.5” ) = 816.8 in2
Note: only 7.5” of deck thickness is structural.
PROPERTIES OF COMPOSITE
BT-72
PROPERTIES OF COMPOSITE
BT-72Haunch – assumed ½” over BT-72 flange width to account
for di fferential camber in the beams.
Transformed Haunch Width = 0.756(42” ) = 31.75 in.
Transformed Haunch Area = 31.75” (0.5”) = 15.87 in2
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PROPERTIES OF COMPOSITE BT-72PROPERTIES OF COMPOSITE BT-72
Atr in2
ybin.
Aybin.3
A(ybc-yb)2
in.4
Iin.4
I+A(ybc-yb)in.4
Beam 767.00 36.60 28072 325484 545894 871378
Haunch 15.87 72.25 1147 3601 0 3601
Deck 816.8 76.25 62280 296420 3829 300249
Sum 1599.7 91500 1175230
ybc = 91500/1599.7 = 57.20 in.(distance to bottom of composite)
PROPERTIES OF COMPOSITE BT-72PROPERTIES OF COMPOSITE BT-72
Ac = 1599 in2
Ic = 1175230 in4
hc = 80 in.
ybc = 91477/1599.4 = 57.20 in.
(distance to bottom of composite)
ytc = 80 – 57.20 = 22.80 in.
(distance to top of composite)ytg = 72 – 57.20 = 14.80 in.
(distance from composite neutral axis to top of
beam)
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PROPERTIES OF COMPOSITE
BT-72
PROPERTIES OF COMPOSITE
BT-72
Composite Section Modulus to Bottom:Sbc = Ic / ybc = 1175230 /57.20 = 20545 in
.3
Composite Section Modulus to Top of
Composite:
Stc = Ic /nytc = 1175230/(0.756*22.8) = 68180 in.3
Note: 1/n converts stress in transformed
concrete to stress in actual concrete.
Composite Section Modulus to Top of Beam:
Stg = Ic / ytg = 1175230 /14.8 = 79400 in.3
DEAD LOADS - DCDEAD LOADS - DC
DC – Applied to precast only.
Beam self weight wg = 0.799 kip/ft.
Slab weight – include ½” integral wearing
surface.
ws = (8” /12” /ft)(12 ft.)(0.150 kcf) = 1.20 kip/ft
Haunch
wh = (0.5” /12)(42” /12)(0.150 kcf) = 0.022 kip/ft
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DEAD LOADS - DCDEAD LOADS - DC
DC – Applied to composite section. To
determine if the barrier weight and the
future wearing surface can be equally
distributed, the following must be met
(LRFD 4.6.2.2.1):
1) Width of deck constant OK
2) Number of beams > 4 OK
3) Curvature < specified in 4.6.2.1.4 OK
straight4) Cross section matches one given in LRFD
Spec. table 4.6.2.2.1-1 OK type “ k”
k
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DEAD LOADS - DCDEAD LOADS - DC5) The overhang of the roadway, from the
outside of the web, de < 3.0 ft.
de = 3 ft OK
Def. of de changed in2008 interim (LRFD 4.6.2.2.1).
DEAD LOADS - DCDEAD LOADS - DC
DC – Applied to composite section
Barrier weight – 0.30 kip/ft
wb = 2 barriers (0.3 k/ft) / (4 beams) =
0.150 k/ft /beam
Diaphragm weight – assumed steel X
braces. Weight ignored in this example.
Typically, they weigh a few hundred
pounds.
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DEAD LOADS - DWDEAD LOADS - DW
DW – Future wearing surface and uti lities.
Future wearing surface 2” @ 0.150 kcf
(2” /12)(0.150 kcf) = 0.025 ksf
0.025 ksf (42’ roadway width) / 4 beams
= 0.263 k/ft /beam
UNFACTORED DEAD LOADSUNFACTORED DEAD LOADS
Al l loads are uniform. DL moments and
shears on the precast can be found from:
0.5
0.5
x
x
V w L x
M wx L x
Use overall length at ini tial (release)condition.
Center to center of bearing at deck
placement.
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UNFACTORED DEAD LOADSUNFACTORED DEAD LOADS
The shears and moments due to the future
wearing surface and the barrier weight are
computed by considering the bridge as a
continuous, three span structure.
The span lengths after continuity is
established are center of support to center of
pier for end spans and center of pier to
center of pier for the middle span.
Shears and moments can be found us ing any
analysis program or by a hand calculation.
Unfactored DL MomentsUnfactored DL Moments
End
Spans
MiddleSpan
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LIVE LOAD DISTRIBUTION FACTORSLIVE LOAD DISTRIBUTION FACTORS
To use distr ibution factors, the following must bemet:
1) Width of deck constant OK
2) Number of beams > 4 OK
3) Curvature < specified in 4.6.2.1.4 OK straight
4) Cross section matches one given in LRFD Spec.
table 4.6.2.2.1-1 OK type “ k”
5) de < 3 f t. OK 3 ft.
6) Beams parallel and approximately same
stiffness. OK
LIVE LOAD DISTRIBUTION
FACTORS - MOMENT
LIVE LOAD DISTRIBUTION
FACTORS - MOMENTNumber of design lanes = integer part of
42 ft. / (12 ft./lane) = 3 lanes
42 ft. is clear roadway width.
Interior Beams (Table 4.6.2.2.2b-1):
0.10.6 0.2
3
0.10.4 0.3
3
0.075
9.5 12
0.0614 12
g
s
g
s
Two Lanes
K S SDFM
L Lt
One Lane
K S SDFM
L Lt
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LIVE LOAD DISTRIBUTION
FACTORS - MOMENT
LIVE LOAD DISTRIBUTION
FACTORS - MOMENT
To use these factors:
1) 3.5’ < S < 16’ S = 12 ft. OK
2) 4.5” < ts < 12” ts = 7.5 in. OK
3) 20’ < L < 240’ L = 120 ft. OK
4) Nb > 4 beams Nb = 4 beams OK
Note: Although this is a 3 lane bridge, there is
NO reduction to the LL for mul tiplepresence. The distribution factors already
account for multiple presence.
LIVE LOAD DISTRIBUTION
FACTORS - MOMENT
LIVE LOAD DISTRIBUTION
FACTORS - MOMENT
2g gc
cs
K n I Ae
E n
E
n = 5072/3834 = 1.3229eg = (7.5/2)+0.5+35.4 = 39.65
= distance between centroids of beam and slab
A = area of non-composi te beam
I = moment of inertia of non-composi te beam
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LIVE LOAD DISTRIBUTION
FACTORS - MOMENT
LIVE LOAD DISTRIBUTION
FACTORS - MOMENT
2g gK n I Ae
Kg = (1.323)[545894 + 767(39.65)2]
= 2 317 340 in4
LIVE LOAD DISTRIBUTION
FACTORS - MOMENT
LIVE LOAD DISTRIBUTION
FACTORS - MOMENT
0.10.6 0.2
30.075
9.5 12
g
s
Two Lanes
K S SDFM
L Lt
S = 12 ft.
L = 120 ft.
Kg = 2 317 340 in
4
ts = 7.5”
DFM = 0.905 lanes/beam
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LIVE LOAD DISTRIBUTION
FACTORS - MOMENT
LIVE LOAD DISTRIBUTION
FACTORS - MOMENT
0.10.4 0.3
30.06
14 12
g
s
One Lane
K S SDFM
L Lt
S = 12 ft.
L = 120 ft.
Kg = 2 317 340 in4
ts = 7.5”
DFM = 0.596 lanes/beam
DFM = 0.905 lanes/beam –two lanes CONTROLS
LIVE LOAD DISTRIBUTION
FACTORS - SHEAR
LIVE LOAD DISTRIBUTION
FACTORS - SHEAR
2
0.212 35
0.3625
Two Lanes
S SDFV
One Lane
SDFV
Interior Beams:
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LIVE LOAD DISTRIBUTION
FACTORS - SHEAR
LIVE LOAD DISTRIBUTION
FACTORS - SHEAR
To use these factors:
1) 3.5’ < S < 16’ S = 12 ft. OK
2) 4.5” < ts < 12” ts = 7.5 in. OK
3) 20’ < L < 240’ L = 120 ft. OK
4) Nb > 4 beams Nb = 4 beams OK
5) 10 000 < Kg < 7 000 000
Kg = 2 317 340 OK
LIVE LOAD DISTRIBUTION
FACTORS - SHEAR
LIVE LOAD DISTRIBUTION
FACTORS - SHEAR
2
0.212 35
0.3625
Two Lanes
S SDFV
One Lane
SDFV
S = 12 ft.
DFV = 1.082 lanes/beam two lane CONTROLS
DFV = 0.840 lanes/beam one lane
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